Rabbit Anti-Mouse CD105/ENG (a.a. 37–332) Polyclonal antibody

The immersed boundary method (IBM) has been frequently utilized to simulate the motion and deformation of biological cells and capsules in various flow situations. Despite the convenience in dealing with flow-membrane interaction, direct implementation of membrane viscosity in IBM suffers severe numerical instability. It has been shown that adding an artificial elastic element in series to the viscous component in the membrane mechanics can efficiently improve the numerical stability in IBM membrane simulations. Recently Li and Zhang (Int J Numer Methods Biomed Eng 35:e3200, 2019) proposed a finite-difference method for calculating membrane viscous stress. In the present paper, two new schemes are developed based on the convolution integral expression of the Maxwell viscoelastic element. We then conduct several tests for the accuracy, stability, and efficiency performances of these three viscous stress schemes. By studying the behavior of a one-dimensional Maxwell element under sinusoidal deformation, we find that a good accuracy can be achieved by selecting an appropriate relaxation time. The twisting sphere tests confirm that, compared to the numerical errors induced by other components in capsule simulations, such as the finite element method for membrane discretization and IBM for flow-membrane interaction, the errors from the viscous stress calculation are negligible. Moreover, extensive simulations are conducted for the dynamic deformation of a spherical capsule in shear flow, using different numerical schemes and various combinations of the artificial spring constants and calculation frequency for the membrane viscous stress calculation. No difference is observed among the results from the three schemes; and these viscous stress schemes require very little extra computation time compared to other components in IBM simulations. The simulation results converge gradually with the increase in the artificial spring stiffness; however, a threshold value exists for the spring stiffness to maintain the numerical stability. The viscous stress calculation frequency has no apparent influence on the calculation results, but a large frequency number can cause the simulation to collapse. We therefore suggest to calculate the membrane viscous stress at each simulation time step, such that a better numerical stability can be achieved. The three numerical schemes have nearly identical performances in all aspects, and they can all be utilized in future IBM simulations of viscoelastic membranes.

We extend the classical SIR model of infectious disease spread to account for time dependence in the parameters, which also include diffusivities. The temporal dependence accounts for the changing characteristics of testing, quarantine and treatment protocols, while diffusivity incorporates a mobile population. This model has been applied to data on the evolution of the COVID-19 pandemic in the US state of Michigan. For system inference, we use recent advances; specifically our framework for Variational System Identification (Wang et al. in Comput Methods Appl Mech Eng 356:44-74, 2019;[cs.CE]) as well as Bayesian machine learning methods.